Fluids and Ping Pong Ball Magnus and Coanda Effect

Given a hairdryer blowing vertically against gravity toward a ping pong ball the ping pong ball is suspended. The ball is relatively stable in the jet because the high velocity of the jet causes a decrease in pressure, causing the ambient air to mix, therefore keeping the ball in the jet rather than flying off sporadically.

If the hair dryer is angled to the right, the ping pong ball still floats. Is this solely due to the above explanation or does the Magnus effect play a role? I was thinking that with the jet toward the right, the ball would spin clockwise, thereby forcing the wake of the ball to the bottom right. The equal and opposite force of the air would then push the ball to the upper left.

As far as I understand, the Coanda effect forces the air to adhere to the curvature of the ball, but can someone explain why this happens and how this force of adhering to the wall differs from the Magnus effect (which seems to explain why the wake redirects)?

Well, for one, the Magnus effect requires the ball to be rotating, and generally fairly rapidly. No rotation, no Magnus effect. The Coanda effect is solely due to the fact that a fluid can't form a void, so a jet near a surface will stick to it.

The Coanda effect is solely due to the fact that a fluid can't form a void, so a jet near a surface will stick to it.

But sometimes flow separates from objects and leaves recirculating flow, not flow that remains attached. How then can we predict when the flow remains attached rather then separates?

Perhaps related, but I know turbulent wakes along a sphere separate later along the sphere's surface than laminar wakes, presumably because the higher momentum near the surface for the turbulent case can resist the wake's adverse pressure gradient further than in the laminar case. Is the Coanda effect related?

But sometimes flow separates from objects and leaves recirculating flow, not flow that remains attached. How then can we predict when the flow remains attached rather then separates?

That flow is still attached in the sense that there is no void touching the surface. There is still air there. That's a different phenomenon known as separation. After all, the Coanda effect isn't all-powerful. Eventually, other factors will be great enough to force the jet to separate from the surface, at which point other fluid is drawn under it so that still no void forms.

When does separation occur? Basically, when a boundary layer experiences an adverse pressure gradient for long enough, it will develop a region of reversed flow near the surface. This is separation.

Perhaps related, but I know turbulent wakes along a sphere separate later along the sphere's surface than laminar wakes, presumably because the higher momentum near the surface for the turbulent case can resist the wake's adverse pressure gradient further than in the laminar case. Is the Coanda effect related?

That's correct. The Coanda effect is related in the sense that a boundary layer forms and undergoes the same exact rules as any other boundary layer. This is why I really hate when people throw around the term "Coanda effect" as if it is some kind of special rule, when really it's just fluids behaving normally. In fact, in all of the fluids courses I have taken or taught, I have never once "learned" or "taught" the Coanda effect. It's just normal fluid motion.

That flow is still attached in the sense that there is no void touching the surface. There is still air there. That's a different phenomenon known as separation. After all, the Coanda effect isn't all-powerful. Eventually, other factors will be great enough to force the jet to separate from the surface, at which point other fluid is drawn under it so that still no void forms.

So am I correct in saying that the Coanda effect occurs everywhere along the ball until separation?

That's correct. The Coanda effect is related in the sense that a boundary layer forms and undergoes the same exact rules as any other boundary layer. This is why I really hate when people throw around the term "Coanda effect" as if it is some kind of special rule, when really it's just fluids behaving normally. In fact, in all of the fluids courses I have taken or taught, I have never once "learned" or "taught" the Coanda effect. It's just normal fluid motion.

Interesting; I've only just learned of it but this is good to know! So you're saying fluids flow around an object 1/2 ways: either the flow remains attached, perhaps due to momentum and inertia overpowering the adverse pressure gradient, or the flow separates, signifying the momentum has decreased to the point where the pressure gradient dominates. Both of these situation arise from fluid "not forming a void", although the former is sometimes referred to as the Coanda effect? Have I said this correct?

Lastly, I saw on a wikipedia page regarding the Coanda effect a picture of a jet with a plate near the bottom side. In a picture a moment later the jet tends toward the plate. Their explanation is that the pressure underside the jet is lower than that above the jet, causing fluid to tend toward the plate. My intuition says since the plate is not moving, no slip implies velocities tend to be lower underside, and hence pressure should be higher, which I feel would push the jet away from the wall. Can you explain this?

I wouldn't say the pressure gradient dominates. Consider the flow over the top of an airfoil, for example. For about the first half, the flow accelerates over the upper surface under the influence of a favorable pressure gradient. That velocity profile is going to look a little "fuller" at the top than what you would expect from a simple Blasius profile. After it passes that top point, called the pressure minimum, it now encounters a region of increasing pressure. Over the rest of the wing, the adverse pressure gradient slowly removes momentum from the boundary layer. If that adverse pressure gradient persists for long enough, it can cause the flow near the wall to reverse, forming a separation bubble.

So it's not a matter of the pressure gradient necessarily dominating. It's really just a matter of the pressure gradient acting over a distance that is large enough that some region of the fluid decelerates back down to zero velocity and then continues on to a negative velocity.